MPPT using PSO Technique Comparing to Fuzzy Logic and P&O
Algorithms for Wind Energy Conversion System
HAYAT EL AISSAOUI1, ABDELGHANI EL OUGLI2, BELKASSEM TIDHAF1
1Renewable Energy Embedded Systems and Artificial Intelligence Team (SEERIA),
Mohammed First University, MOROCCO
2Computer Science, Signal, Automation and Cognitivism Laboratory (LISAC)
Faculty of Science Dhar El Mahraz Sidi Mohamed Ben Abdellah University,
MOROCCO
Abstract: - This paper proposes a new maximum power point tracking (MPPT) technique for wind turbine
Connection to a permanent magnet synchronous generator (PMSG), based on the Particle Swarm Optimization
(PSO) algorithm. The PSO technique aims to control the boost converter by calculating the duty cycle value
based on the voltage and current values. The Wind Energy Conversion System (WECS) includes a wind
turbine, a PMSG, rectifier and a DC/DC boost converter that is connected to a load. To verify the performance
of the suggested algorithm PSO, The results of the simulation are compared with those of fuzzy logic and
(Perturb and Observe)P&O techniques, under step wind variations, using MATLAB/SIMULINK. The results
of the simulation show that the proposed PSO technique ensures a good tracking of the maximum power point
as the results obtained are more stable and the oscillations are eliminated.
Key-Words: Wind Turbine, PMSG, WECS, PSO, Fuzzy Logic, P&O.
Received: June 25, 2021. Revised: April 27, 2022. Accepted: May 26, 2022. Published: July 5, 2022.
1 Introduction
The consumption of energy worldwide is principally
covered by the fossil fuels (oil, coal, natural gas and
nuclear) which are having a negative impact on the
environment. [1]-[4]. Climate change, as one of the
major problems facing humanity in this century, is
caused by greenhouse gas emissions, in particular
by the combustion of fossil fuels [1,2]. Considering
the evolution of the actual standard of living of
human beings, the increase in energy demand has
allowed a significant development of renewable
energies [5]. These clean and durable energies have
become very important because they are considered
an alternative to fossil fuels, which are decreasing,
that meet the objectives of the Kyoto protocol. [4]
Renewable energies are clean and natural sources
of energy, coming from the sun (photovoltaic), wind
(wind turbine), geothermal, waterfalls, tides or
biomass, capable of satisfying most of our needs.
Their use generates almost no waste and polluting
emissions. Wind energy systems are the fastest
growing technology. Indeed, Wind energy is among
the largest sources of renewable energy in the world.
For efficient functioning of WECS, various
maximum power point tracking (MPPT) strategies
are developed in the literature [6]. These algorithms
can be categorized into two types, The first category
includes techniques such as optimal torque (OT) [7],
top speed ratio (TSR) [8]... this type of algorithms
control the electrical power output of WTs through
maximization the mechanical power generated by
the wind. While the second category maximizes
directly the electrical power produced at the output.
TSR is characterized by its simplicity and speed
of response, however, its performance dependent on
the measurement techniques or the precision of the
wind speed estimation. L’OT is an effective and
simple technique which does not require any
previous knowledge of wind speed. However, it is
based on optimal torque curves or look-up tables
based on experiments.
The second category of MPPT algorithms
consists of strategies such as incremental
conductance (IC), hill-climbing search (HCS) [9],
[10], perturbation and observation (P&O) [11]. In
the literature there are also smart MPPT algorithms
based on artificial intelligence techniques
particularly fuzzy logic controllers (FLC) and
artificial neural networks (ANN).[12]
Many published papers have been compared
between several MPPT techniques for WECS, for
example in [13], three MPPT controllers P&O, PI
and FLC are modeled for wind power and the output
is compared under a varying wind speed conditions,
The efficiency of each controller is evaluated and
the authors have concluded that the FLC controller
is more efficient and more reliable than the P&O
and PI controllers.
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In this paper we propose new MPPT technique
based on the PSO technique, the results of this
algorithm will be compared to the FL and P&O
techniques. For this purpose we have proposed a
system that contains a wind turbine connected to a
synchronous machine, a rectifier, and a boost
converter, as shown in Figure1. The results of three
controllers are verified in MATLAB/Simulink for
different wind speed values.
Fig. 1: Diagram of MPPT in WT system
The paper is organized as follows:
Section 2 presents the modeling of the wind
power system. Section 3 is about the converter
modeling. Section 4 explains the proposed
approaches. Section 5 deals with the results obtained
and the efficiency of the proposed algorithms,
section 6 presents the conclusion.
2 Modelling of a Wind Turbine
A wind turbine is therefore a system that is able to
transform the kinetic energy of the wind into
mechanical or electrical energy. This kinetic energy
is received by the blades of the turbine before being
transformed into mechanical energy, which in turn
is transformed by a synchronous or asynchronous
generator into electrical energy. The classification of
wind turbines is based on the orientation of the axis
of rotation in relation to the wind direction
(horizontal or vertical). For the model proposed in
this paper we have chosen to work with a turbine
connected to a synchronous generator.
The aerodynamic power P (a) extracted by the
turbine rotor is expressed, in general, in terms of the
power coefficient Cp and is given by the following
expression: [14]
(1)
Where R means the turbine ratio, is the wind
speed (m/s).
The parameter Cp is dimensionless. This
characteristic parameter of the wind turbine is a
non-linear function depending, on the wedge angle β
and the specific speed λ. the latter is represented as
the ratio between the tangential speed of the blade
tip and the wind speed.
(2)
The power coefficient is given below:
(3)
(4)
The kinetic energy of the wind that is extracted
by the aero-turbine is converted into mechanical
power which is translated into a driving torque Ta
making the rotor rotating at a speed ω. the
expression of the aerodynamic torque can be written
in the following form:
(5)
The following figure describes the relationship
between the variation of the power coefficient and
the tip ration speed λ for different values of β:
Fig. 2: Characteristics of power coefficient.
The figure 3 shows the variation of the
mechanical power of the wind turbine, as a function
of the variation of the rotation speed for different
wind speed values, and that for the turbine used in
this paper:
Fig. 3. The power curves under different wind
speeds (β=0).
The parameters of the turbine generator used in
this paper are listed in the table 1:
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Table 1. WT generator system characteristics
3 Converter Modelling
Emerging electronic devices must meet certain
criteria such as high quality, reliability, size, weight
and low cost. Linear power regulators, whose
functioning principle is based on a current or
voltage divider, can give a very high quality output
voltage. However, this type of regulator remains
ineffective because their principal area of use
involves low power levels.
Switching regulators or DC/DC converters use
electronic switches, based on semiconductors such
as: thyristor, power transistor or IGBT...etc, because
they generate a low power loss when switching from
one state to another. These converters assure high
energy conversion efficiencies and they can be used
at high frequencies. The dynamic characteristics of
DC/DC converters increase with higher operating
frequencies. [15]
DC/DC converters are the main part of a MPPT
system. They are used to convert an unregulated DC
input to a regulated DC output voltage, in our case
presented in this paper, the DC/DC converter is used
as an interface between the wind model and the load
to ensure that the WT model operates at its
maximum power point, and this is achieved through
the control of the duty cycle D using the MPPT
algorithms. There are many topologies of DC-DC
converter used today, such as Buck, Boost, Buck /
Boost, CUK and Sepic. In this paper we chose a
boost converter. [16]
Figure 4 shows a boost converter that converts
the input DC voltage to a higher output voltage.
Fig. 4: Configuration of Boost converter.
The boost structure includes a switch which is
controlled for firing and blocking (bipolar, MOS or
IGBT), a diode and at least one energy storage
element (capacitor and/or inductor).
The filters are composed of capacitors that are
added to the output of the converter to minimize the
output voltage ripple; the inductor is placed in series
with the input source to minimize the current ripple.
The series resistance mimics the aggregate ohmic
losses introduced by the parasitic resistances of the
inductor. The continuous conduction mode of a
boost converter has two states for each commutation
cycle. The circuit operates by changing the states of
the diode and the switch between ON and OFF.
When the switch is on, the diode is automatically
turned off, as its voltage becomes negative. Also,
when the switch is off, the diode is turned on. Such
behavior is controlled using the duty cycle signal
that controls the IGBT, can take normalized values
between 0 and 1.
Case1: The transistor is in the ON state and the
diode is in the OFF state.
During this phase, the inductance L stocks energy,
which gives us the following equations:
RL
(6)
(7)
Case 2: the transistor is in the OFF state and the
diode is in the ON state.
The switch opens so the only path for the
inductor current to pass is through the D diode and
the parallel combination of capacitor and load. This
allows the capacitor to transfer the energy acquired
during the operating period. The state functions then
become:
(8)
(9)
The combination of the two steps gives us
the following equations:
The ratio that relates the input and output
voltage is defined by :
(10)
Characteristics
Values
Rated Voltage
90 V
Rated Power
1000W
Synchronous
inductance
1mH
Rated Current
4.8A
Number of poles
8
Synchronous resistance
1.13Ω
Friction coefficient
0.006N.m.s/rad
Magnetic flux
0.16Wb
Moment of inertia
0.005N.m
Blade length
1.2m
Air density
1.2 kg/ m3
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D is the duty cycle.
The inductance of the boost converter, L, is
calculated as follows:
(11)
Where
L
i
is the current ripple in the inductor
and is the switching frequency.
The value of the output capacitor is given as
follows:
(12)
out
I
and
out
V
successively the output current and
the output voltage ripple.[16]
4 MPPT Controllers
4.1 Proposed PSO MPPT Technique
The PSO technique was inspired by Russel Eberhart
and James Kennedy from the behavior of birds,
during a computer simulation of grouped flights of
birds and schools of fish.[17]
The swarm of particles is a population of simple
agents, called particles. The swarm of particles is a
population of simple agents, called particles. The
principle of the PSO algorithm is to move the
particle to find its best position. In the first step, the
particles are positioned in a search space in a
random way. Each of these particles is characterized
by a speed that allows it to move, and during the
iterations, the particle changes position according to
its previous position, its neighbor and its best
position, at the end of these iterations the particle
can fall on its best position.
Fig. 5: Principle of the movement of a particle
At the beginning of the algorithm, the particles of
the swarm are initialized in a random/regular way in
the search space. Then, for each iteration the
particles move.
The position of the particle is corrected
according to its updated speed (velocity), the best
personal position obtained (PBest) and the best
position obtained in the neighborhood (GBest). The
PSO is based on the rules of updating the local and
global positions of particles and the group, given by
the equations: [18]
(13)
(14)
c1 and c2 are acceleration constants.
P : Position of the particle.
V: Velocity.
PBest: Best position of the particle which
corresponds to Local_Dbest.
GBest : Best position of the group of particles which
corresponds to Global_Dbest.
r1 and r2: Random variable uniformly distributed
on an interval of [0, 1] (function defined in Matlab).
D: Duty cycle.
In our case, the objective of the PSO technique is
to calculate the Duty cycle value D, based on the
power value P calculated from the inputs V, I.
In order to find the optimal value of D, we
implemented the PSO algorithm in this paper as
follow:
Measure V,I.
Calculate P.
Initialize the size of the swarm, the maximum
number of iterations, and the PSO constants
c1, c2 and w; determine the random numbers
r1 and r2.
Attribute the value Zero to the previous and
new Powerbest vectors:
(15)
Initialize the Duty Cycle value.
Initialize velocity:
(16)
Update of the velocity value using the PSO
parameters described in table 2, and calculate
its final value:
(17)
d,
gwbest (18)
(19)
calculate the final value of the duty cycle:
(20)
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The following table includes the PSO parameters
we have chosen during the simulation:
Table 2. PSO parameters
4.2 P&O Controller
Among the classical techniques used for MPPT
research for a wind turbine system, we find in the
literature the P&O technique which is a famous
algorithm widely used in research papers because of
its simplicity, and its ease of implementation. We
have chosen this algorithm to validate the PSO
technique proposed in this paper.
The following diagram explains the functioning
principle of this algorithm to find the MPPT for a
wind system connected to a PMSG. The objective of
the P&O technique is to calculate the Duty cycle
value D, based on the value of DeltaP, DeltaV
calculated from the inputs V, I.
Fig. 6: Perturb and Observe Approach (P&O)
The P&O algorithm, in spite of its known
advantages, also presents a problem of oscillations
around the MPP which is produced in permanent
regime and this is caused by the MPP search process
that must be repeated regularly, which obliges the
system to oscillate continuously around the MPP.
[19]
The principle of the P&O technique is to perturb
the voltage by a small amplitude around its initial
value and to analyze the behavior of the resulting
power variation. If a positive increment of the
voltage generates an increase of the power, it means
that the operating point is to the left of the PPM. If,
on the other hand, the power decreases, this means
that the system has surpassed the PPM. The same
reasoning can be applied when the voltage
decreases. Based on these different analyses it is
then easy to situate the operating point in regard to
the PPM, and to make it converge towards the
maximum power through an appropriate control
order.
In another way we can say that the principle is as
follows: at the beginning the voltage V is perturbed,
then we measure the power supplied by the WT at
the output of the rectifier at the moment k, and then
we compare it to the preceding one at the moment
(k-1). If the difference is positive, the power is
increasing, it means that we are approaching the
MPP and that the change of the duty cycle is kept in
one direction. On the other hand, if the difference is
negative, the power is decreasing, we are moving
away from the MPP. We must therefore reverse the
direction of the variation of the duty cycle.
4.3 Fuzzy Logic Controller
FL is a new approach based on artificial
intelligence. FL represents an improvement of the
classical IC algorithm in terms of robustness,
stability and ease of implementation. Like other
MPPT controllers, the main task of the FL controller
is to achieve the MPP. However, the performance of
this controller depends mainly on human expertise.
The FL approach is derived from decomposing a
range of variation of a real variable into linguistic
variables and assigning the membership function for
each variable. The rules developed from the human
operator's expertise are expressed in linguistic form.
These rules determine the dynamic performance of
the FL controller. The proposed FL controller
consists of four basic components: fuzzification
unit, basic rules inference engine and
Defuzzification.[15]
Fuzzification: Convert numeric input variables
into linguistic variables based on a membership
function. Before fuzzifying the data, it must first be
normalized to match the range of the universe of
discourse that is appropriate for the controller input.
Rule base: Before starting this phase ,the user
must define the fuzzy set database which consists of
defining the fuzzy sets of input and output variables,
the partition of the input and output fuzzy space, and
the choice of membership functions that describe
the fuzzy sets of input and output variables
The fuzzy rules describe the relationship between
the output and the input of the fuzzy control. These
fuzzy rules encode an expert's knowledge of the
symbol
value
Weight of local
information
C1
0.1
Global information weight
C2
0.1
Weight of inertia
W
0.5
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process control in linguistic terms in the general
form of "if premise then conclusion", where the
premises relate to the inputs of the fuzzy controller
and the conclusions relate to the outputs. The
number of fuzzy rules depends, in particular, on the
partition of the universes of discourse of the input
and output variables.
Inference: A fuzzy inference is a relation defined
between fuzzy subsets. This fuzzy relation can
intervene any fuzzy operator.
Defuzzification is the process of converting a
linguistic value into a numerical value. [19]
The Fuzzy Logic Controller process for our case
is illustrated in Figure 7.The objective of the Fuzzy
Logic technique is to calculate the Duty cycle value
D, based on the Delta P, Delta V.
Fig . 7: Structure of a fuzzy controller.
The inputs DeltaP and DeltaV are represented by
the equations given below:
DeltaP (k) =P(k)-P(k -1) (16)
DeltaV (k) =V(k)-V(k -1) (17)
The membership functions of DeltaP, DeltaV
and D are respectively shown in Figure 8 (a), Figure
8 (b) and Figure 8 (c).
(a)
(b)
(c)
Fig . 8: Membership functions related to (a) DeltaP, (b)
DeltaV, (c) D.
Table 3 gives the inference rules for different
combinations of the input variables DeltaP, DeltaV
with the output duty cycle D.
Table 3. Inference Rules related to Fuzzy Logic
WT.
5 Simulation and Discussion
In this section, we will compare through
simulations, the convergence to MPP using one of
the three techniques "P&O", "Fuzzy Logic" and
"PSO", for a wind energy conversion system. This is
achieved by simulation under Matlab/Simulink, as
shown in the following figure:
Fig . 9: The proposed model in Matlab/Simulink.
The system contains the following components:
wind turbine, permanent magnet synchronous
generator (PMSG), rectifier, boost converter,
controllers block (P&O/Fuzzy Logic/PSO). The
wind speed varied in three steps, from 8.5 m/s to 8.1
m/s, then to 7.9 m/s. As shown in the figure 10.
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Fig. 10: Wind speed variation.
Figures 11, 12, 13 show respectively the Cp
curve for wind speed values varying between
8.5m/s, 8.1m/s, and 7.9m/s, using respectively the
FL, P&O, PSO techniques.
Fig. 11: Power Coefficient curve using PSO
Controller.
We notice from the evolution of Cp that the PSO
technique allows us to continue the MPP because
the Cp reaches the maximum value 0.48 which
means that the power produced by the system is
maximal, and this is with a high stability and with
an absence of any oscillations.
Fig. 12: Power Coefficient curve using Fuzzy Logic
Controller
We see from the evolution of Cp that the FLC
technique allows us to continue the MPP because
the Cp reaches the maximum value 0.48 but with
some oscillations.
Fig. 13: Power Coefficient curve using P&O
Controller.
We can see from the evolution of Cp that the
P&O technique does not allow us to continue the
MPP for all the tested wind speed values because
the Cp does not always reach the maximum value of
0.48, and we notice that this technique presents a
considerable rate of oscillations.
Figures 14, 15, 16 show respectively the
mechanical power curve for wind speed values
varying between 8.5m/s, 8.1m/s, and 7.9m/s, using
respectively the PSO, FL, P&O techniques.
Fig. 14: Variation of the mechanical power using
PSO controller.
Fig. 15: Mechanical Power using Fuzzy Logic
Controller
Fig. 16: Mechanical Power using P&O
controller.
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Comparing the curves of evolution of the power
produced by WT using respectively PSO, FL, P&O,
controllers, with the characteristic of the turbine
(figure 3), we deduce that the PSO technique allows
reaching the maximum power for each value of
wind speed with a high stability more than the FL
and P&O techniques.
Fig. 17: The variation of the voltage at the
output of the boost converter, using PSO
controller.
6 Conclusions
The objective of this paper is to design a new MPPT
control based on the PSO technique for a WECS
system. This paper proposes to analyze the selected
MPPT methods (PSO, FL and P&O) and to evaluate
their behaviors in terms of stability, efficiency in
order to compare them. The simulation is performed
for variable wind speed values.
The PSO technique is used to control the boost
converter by determining the duty cycle value as a
function of the voltage and current values.
The simulation results revealed that PSO ensures
a good tracking of the maximum power point and it
provides more efficient and stable results compared
to the other proposed methods P&O and FL, the
PSO technique eliminates all oscillations presented
by P&O and FL.
The proposed and studied controllers are
implemented in Matlab/Simulink to obtain the
output response of the developed system.
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